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Verbeia♦Aug 2 '12 at 21:28

belisarius' suggestion, to use Plot[-Log[-Evaluate[B[t] /. model]], {t, 1952, 1970}] to see what is going on, is a good one.

Mathematica is probably refusing to draw the plot when PlotRange->All because it can't come up with a sensible set of ticks / divisions to capture a function that exponentiates like that.

Judging by the size of the units you are using, I am going to guess that this is an attempt at an economic model using GDP or some other quantity measured in the billions and trillions. If so, I would suggest carefully examining the parameters to make sure you haven't slipped a few zeros somewhere. In particular, the parameters $562.86$ seems way too big to generate a sensible non-explosive system.

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